Block #346,237

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 10:38:10 AM · Difficulty 10.2220 · 6,450,048 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

2c37cb01c1698e3c3fab9360b98a5921a803032bf2559a1f41afcd6ec5c00b53

View on Chainz ↗

Height

#346,237

Difficulty

10.221967

Transactions

Size

934 B

Version

Bits

0a38d2d0

Nonce

149,941

Timestamp

1/6/2014, 10:38:10 AM

Confirmations

6,450,048

Mined by

⛏️ }HaRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

f5af9f99e72d92bf8af9548f0f6897ee9ed74d6e37dcb0ef5d5c618ea6048d8d

Transactions (1)

Coinbasef5af9f99e72d92…5c618ea6048d8d

1 in → 23 out9.5600 XPM845 B

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AFutDVqJ…TJTJj6UF Ae58nAEb…GFUA15fv AP5UvYhU…vLTDwkdA

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.648 × 10⁹¹(92-digit number)

16487111130875743524…86521565703137691839

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.648 × 10⁹¹(92-digit number)

16487111130875743524…86521565703137691839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.648 × 10⁹¹(92-digit number)

16487111130875743524…86521565703137691841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

3.297 × 10⁹¹(92-digit number)

32974222261751487048…73043131406275383679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.297 × 10⁹¹(92-digit number)

32974222261751487048…73043131406275383681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

6.594 × 10⁹¹(92-digit number)

65948444523502974096…46086262812550767359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.594 × 10⁹¹(92-digit number)

65948444523502974096…46086262812550767361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.318 × 10⁹²(93-digit number)

13189688904700594819…92172525625101534719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.318 × 10⁹²(93-digit number)

13189688904700594819…92172525625101534721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.637 × 10⁹²(93-digit number)

26379377809401189638…84345051250203069439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.637 × 10⁹²(93-digit number)

26379377809401189638…84345051250203069441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer